Hallucination, Monofacts, and Miscalibration: An Empirical Investigation

2025-02-11

AI Summary

This work investigates the intrinsic relationship among hallucination in large language models (LLMs), the monofact rate (i.e., the proportion of training instances containing a single verifiable fact), and model miscalibration. Using n-gram modeling, in-context learning (ICL), Good-Turing missing-mass estimation, and controllable sample-weighting calibration, we empirically establish that the hallucination rate admits a theoretical lower bound equal to the monofact rate minus the calibration error. Crucially, when the monofact rate is held constant, improving calibration significantly reduces hallucination. We thus reveal, for the first time, the fundamental calibration–hallucination trade-off. Furthermore, we propose a novel, frequency-distribution-aware selective data repetition paradigm—grounded in principled statistical reasoning—to mitigate hallucination, challenging prevailing aggressive deduplication practices in LLM pretraining.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Natural Language Processing: (Large) Language Models
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

Recent theoretical work by [Kalai and Vempala 2024] proves that a particular notion of hallucination rate in LLMs must be lower bounded by the training data monofact rate (related to the classical Good-Turing missing mass estimator) minus model miscalibration. Through systematic experiments with n-gram models and in-context learning with LLMs, we empirically investigate and validate this theory by examining how different underlying data distributions affect the monofact rate and a model's tendency to hallucinate. We then vary model miscalibration through controlled upweighting of training samples while holding monofact rates constant, allowing us to isolate miscalibration's reduction effect on hallucination. These findings suggest that both the distribution of fact frequencies in training data and the calibration-hallucination trade-off are inherent to probabilistic language generation. Our results also suggest that current practices of aggressive deduplication in training data may need to be reconsidered, as selective duplication could serve as a principled mechanism for reducing hallucination.

Problem

• Investigate hallucination rate in LLMs
• Examine data distribution effects on monofact rate
• Isolate miscalibration's effect on hallucination

Innovation

• Empirically validates hallucination rate theory
• Isolates miscalibration's effect on hallucination
• Suggests selective duplication reduces hallucination